Dualities in lattice Gauge theories

• Grant number: 13/02662-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2013
• End date: February 28, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Paulo Teotonio Sobrinho
• Grantee: Alysson Ferreira Morais
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Using a mathematical formalism borrowed from topological field theory weassociate a vector space H with a two-dimensional structure of algebra and co-algebrafor each model studied. A procedure already developed for G = Z2 allows us,by performing a chage of basis on H to obtain a new model equivalent to thefirst. However, this procedure does not extend to the groups G = Zn, n> 2.In this project, we intend to generalise it for the case of G = Zn in 2D and 3D lattices.In this case, we expect to obtain, for each element of the group GL (n, R), a duality relation.The formalism to be used in this project is a breakthrough in the study of dualitiesin the sense that, usually, we need to study them by applying a sequence ofcombinatorial moves, as "decoration transformation" and "square transformation star" in aspecific way for each model considered. With this generalised algebraic formalism, dualitiescan be derived with a single standard procedure. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MORAIS, Alysson Ferreira. A tensorial approach to the study of dualities between lattice spin models. 2014. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Física (IF/SBI) São Paulo.